LCHL Maths – Sequences and Series, Patterns and Limits

Leaving Cert Higher Level Maths LCHL Maths – Sequences and Series, Patterns and Limits

LCHL Sequences and Series

Your progress through this topic0 of 12 lessons

Lessons in this topic

All 12 lessons, in order — each one ticks off as you open it.

1Arithmetic Sequences 1 2Arithmetic Sequences 2 3Arithmetic sequences 3 4Arithmetic Sequences 4 5Geometric Sequences 1 6Geometric Sequences 2 7Geometric Sequences 3 8Geometric Sequences 4 9Geometric Sequences 5 10Prove the Sum of Geometric Series by induction 11Quadratic Patterns 12Cubic patterns

Common differences

Linear pattern — common first difference — Linear pattern — common first differencethe 1st differences are constant

Quadratic pattern — common second difference — Quadratic pattern — common second differencethe 2nd differences are constant

Cubic pattern — common third difference — Cubic pattern — common third differencethe 3rd differences are constant

Patterns & tests you must know

Quadratic pattern — Quadratic pattern2a = second difference

Cubic pattern — Cubic pattern6a = third difference

Three terms in an arithmetic sequence — Three terms in an arithmetic sequencemiddle term is the average

Three terms in a geometric sequence — Three terms in a geometric sequenceT₃/T₂ = T₂/T₁

Prove a sequence is arithmetic — Prove a sequence is arithmeticconstant first difference

Prove a sequence is geometric — Prove a sequence is geometricconstant ratio

The rules of limits — The rules of limitssum, product & quotient rules

Key ideas in this topic

Arithmetic — nth term — Arithmetic — nth termSequences & Series

Arithmetic — sum of n terms — Arithmetic — sum of n termsSequences & Series

Geometric — nth term — Geometric — nth termSequences & Series

Geometric — sum of n terms — Geometric — sum of n termsSequences & Series

Sum to infinity — Sum to infinitySequences & Series

Check it against the exam

Jump straight to the fully worked solution for that paper.

2023 Paper 1 Q2 →2023 Paper 1 Q9 →2022 Paper 1 Q9 →2021 Paper 1 Q7 →2020 Paper 1 Q2 →

Topic Content

0% Complete 0/15 Steps

Patterns 1: Quadratic Patterns

Patterns 2: Cubic patterns

Sequences and Series 1: Arithmetic Sequences 1

Sequences and Series 2: Arithmetic Sequences 2

Sequences and Series 3: Arithmetic sequences 3

Sequences and Series 4: Arithmetic Sequences 4

Sequences and Series 5: Geometric Sequences 1

Sequences and Series 6: Geometric Sequences 2

Sequences and Series 7: Geometric Sequences 3

Sequences and Series 8 : Geometric Sequences 4

Sequences and series 9: Geometric Sequences 5

Sequences and Series 10: Prove the Sum of Geometric Series by induction

Convergence, Divergence, Continuity and Limits

Proof of Sum to infinity of Geometric sequences